The 21-year-old had a highly successful campaign on loan at Bolton Wanderers last season where he scored eight goals in 12 matches.
Villas-Boas is keen to keep Sturridge at Stamford Bridge this season and the striker is desperate to impress.
"The manager has given me licence to express myself,” he told The Guardian.
"I've never had that before with any manager. He's let me off the leash, if you like, and not just me - everyone feels like that."
The 33-year-old manager joined Chelsea after winning the treble in his first season in charge at Portuguese club Porto.